Details

sample43.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify658.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
4	2001
3	641
2	119
1	36
0	15

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
0.0b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
0.1b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
3.6b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
586×	`*-un-lft-identity`
340×	`add-sqr-sqrt` `add-cube-cbrt`
123×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
29×	`flip3-+` `flip-+`
27×	`div-inv`
20×	`add-cbrt-cube` `add-exp-log`
13×	`add-log-exp`
10×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`sum-log`
4×	`pow1` `insert-posit16` `associate-/l/`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+l+`

Counts

4 → 469

Calls

4 calls:

118.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
288.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
417.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
248.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (+ (+ alpha beta) (* 2 1)) 1.0)
165.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))
186.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0))
119.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.6s

Counts

481 → 481

Iterations

Iter	Nodes
done	2005
2	2005
1	1435
0	606

prune4.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.9b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))

3.6b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

rewrite855.0ms

Algorithm

rewrite-expression-head

Rules

954×	`times-frac`
827×	`*-un-lft-identity`
382×	`add-sqr-sqrt` `add-cube-cbrt`
253×	`distribute-lft-out`
82×	`associate-/l*`
66×	`associate-/r/`
36×	`flip3-+` `flip-+`
31×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/r*`
10×	`cbrt-undiv` `div-exp`
4×	`frac-add` `associate-/l/`
3×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`

Counts

3 → 518

Calls

3 calls:

237.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

342.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))

249.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

series453.0ms

Counts

3 → 9

Calls

3 calls:

168.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1)))

188.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))

96.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1)))

simplify1.9s

Counts

527 → 527

Iterations

Iter	Nodes
done	2004
2	2004
1	1511
0	616

prune6.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.9b

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ beta alpha) (+ beta alpha))
0.0b	(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* (+ beta alpha) (+ beta alpha)) 4)) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1))))
0.1b	(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* (+ beta alpha) (+ beta alpha)) 4)) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))
15.6b	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* (+ beta alpha) (+ beta alpha)) 4))

rewrite752.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
59×	`add-sqr-sqrt`
50×	`times-frac`
38×	`add-cbrt-cube` `add-exp-log`
36×	`add-cube-cbrt`
26×	`associate-l`
21×	`distribute-lft-out`
19×	`associate-r`
14×	`cbrt-undiv` `div-exp`
13×	`pow1` `flip3-+` `flip-+`
12×	`associate-/r/`
9×	`associate-/r*` `prod-exp` `cbrt-unprod` `difference-of-squares`
6×	`frac-times` `swap-sqr`
5×	`associate-/l*` `unswap-sqr` `associate-/l/`
4×	`associate-l/` `frac-add` `associate-r/` `insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `flip3--` `pow-prod-down` `*-commutative` `flip--`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 185

Calls

4 calls:

33.0ms	(* (+ beta alpha) (+ beta alpha))
354.0ms	(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* (+ beta alpha) (+ beta alpha)) 4)) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1))))
211.0ms	(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* (+ beta alpha) (+ beta alpha)) 4)) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))
151.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* (+ beta alpha) (+ beta alpha)) 4))

series815.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (+ beta alpha) (+ beta alpha))
328.0ms	(* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* (+ beta alpha) (+ beta alpha)) 4)) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1))))
280.0ms	(/ (* (/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* (+ beta alpha) (+ beta alpha)) 4)) (/ (- (+ alpha beta) (* 2 1)) (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (+ (* 2 1) 1.0)))
185.0ms	(/ (+ 1.0 (+ (* alpha beta) (+ beta alpha))) (- (* (+ beta alpha) (+ beta alpha)) 4))

simplify1.4s

Counts

197 → 197

Iterations

Iter	Nodes
done	2003
2	2003
1	1153
0	338

prune2.6s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
0.6b	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
1.6b	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
2.7b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

3718×	`times-frac`
2278×	`*-un-lft-identity`
1580×	`add-sqr-sqrt` `add-cube-cbrt`
1263×	`sqrt-prod`
349×	`distribute-lft-out`
206×	`associate-/l*`
128×	`associate-/r/`
110×	`sqrt-div`
72×	`div-inv`
65×	`flip3-+` `flip-+`
44×	`add-exp-log`
31×	`div-exp`
29×	`add-cbrt-cube`
23×	`associate-/r*`
16×	`cbrt-undiv`
6×	`1-exp`
5×	`associate-/l/`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp`
2×	`rec-exp`

Counts

4 → 1628

Calls

4 calls:

464.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
203.0ms	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
343.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
293.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

series923.0ms

Counts

4 → 12

Calls

4 calls:

343.0ms	(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1))) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
175.0ms	(/ (/ (/ 1 (sqrt (+ (+ alpha beta) (* 2 1)))) 1) (sqrt (+ (+ (+ alpha beta) (* 2 1)) 1.0)))
257.0ms	(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1)))) (+ (+ alpha beta) (* 2 1)))
147.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2 1))))

simplify3.1s

Counts

1640 → 1640

Iterations

Iter	Nodes
done	2000
1	2000
0	1681

prune28.7s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.9b

regimes170.0ms

Accuracy

53.7% (1.1b remaining)

Error of 2.3b against oracle of 1.2b and baseline of 3.6b

bsearch146.0ms

Steps

Iters	Range		Point
8	1.3778561594943785e+141	9.602781638389914e+144	9.447545610483609e+144

simplify12.0ms

Iterations

Iter	Nodes
done	40
1	40
0	28

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
282.0ms	8000×	pre	80	true